Keep object in the middle of two other animated objects
This is easy to achieve with the Copy Location constraint.

Select the turret and add two Copy Location constraints - set the target Object of one of them to the first Empty and the other to the second Empty. Then simply slide the Infuence on the second constraint to 0.5 and the turret should move into the middle of the two empties.

The first constraint is simply to ensure that the start point is at the first empty (you could alternatively move it there manually and parent it to the first empty - then you would no longer need that first constraint). The second constraint moves it from its current location (the first Empty) towards the second Empty but the reduced influence means that it only actually moves half way there.